Two large charged plane sheets of charge densities `sigma and - 2sigma C//m^(2) ` are arranged vertically a separation of d between them. Deduce expressions for the electric field at points
to the left of the first sheet ,
(ii) To right of the second sheet,
between the two sheets.

Explanation

Consider two large charged plane sheets of surface charges densities `+sigma and -2 sigma ` arranged vertically with a separation .d. between them.
At any point `P_1` left of first sheet ,electric field due to the two sheets are `E_1 =(sigma)/( 2 in _0) and E_2 (2sigma )/(2 in _0) =(sigma )/( in_0) ` and their directions are mutually opposite as shown here .
` therefore ` Net electric field at ` P_1 , E=E_2-E_1=(sigma )/(in_0) -(sigma )/( 2 in _0) =(sigma )/( 2 in _0) `
towards the first sheet.
(ii) At any point ` P_2` right of second sheet `E_1 =(sigma )/( 2 in _0) and E_2 =(sigma )/( in_0) `
and their directions are again mutually opposite as shown
` therefore ` Net electric field at `P_2 ,E =E_2 -E_1 =(sigma )/( in_0) -(sigma)/( 2 in _0) =(sigma)/ (2 in _0) ` towards the second sheet.
(iii) At a point `P_3` between the two sheets both ` E_1 and E_2` are directed in same directions . Hence net electric field at ` P_3 , E= E_1+E_2 =(sigma)/( 2 in _0) +(sigma)/(in_0) =(3 sigma )/( 2 in _0) ` towards the second sheet.